Contributor
Posts: 26

# Nonlinear Mix Integer Optimization

Hi All,

Does proc optmodel support nonlinear mix integer optimization problem?

I have formulated the problem and model in Proc Optmodel. I am getting following error message

– “ERROR: The NLP solver does not allow integer variables.”

Lokendra

SAS Employee
Posts: 571

## Re: Nonlinear Mix Integer Optimization

PROC OPTMODEL does not (yet) support mixed integer nonlinear optimization, so the error message is expected.  Such problems can often be either linearized or solved indirectly.  Can you please share your data and code?

Contributor
Posts: 26

## Re: Nonlinear Mix Integer Optimization

A representative expression is

Demand  = Constant x (RecommendedPrice/FullPrice)^(-1.8) x (CompetitorPrice/FullPrice)^(-1.5)

RecommendedPrice is a decision variable and Revenue = Demand x RecommendedPrice is in the objective function.

We have some logical constraints on RecommendedPrices which we are modeling using binary variables. The actual problem has many products for which we are determining the price and there are relationships among these prices which are either logical (leading to binary variables) or linear.

As now we know Proc Optmodel does not support this kind of problem.  We are trying to use Proc OPTLSO.  We are trying to use proc optmodel to generate QPS or MPS data but since this is not quadratic problem and also not a linear problem we get error.  In the support they suggest to use Proc FCMP to produce problem statement and use OPTLSO to solve.  Is there any otherway to get the expanded form of probelm.

thanks

Lokendra

SAS Employee
Posts: 571

## Re: Nonlinear Mix Integer Optimization

To use PROC OPTMODEL to generate MPS or QPS, you must remove the nonlinear parts and handle them separately with PROC FCMP, as in this doc example: Example 3.6 Using Nonlinear Constraints

Alternatively, what you have shown so far can be linearized by taking logs, with LogDemand and LogRecommendedPrice as your decision variables:

LogDemand  = log(Constant) -1.8 (LogRecommendedPrice - log(FullPrice)) -1.5 (log(CompetitorPrice) - log(FullPrice))

LogRevenue = LogDemand + LogRecommendedPrice

If the full problem can be linearized, you can use the MILP solver in PROC OPTMODEL.  If you provide the full code and data, I'll take a look.

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